Prof. Martin H. Gutknecht
Seminar for Applied Mathematics
ETH Zurich
ETH-Zentrum, HG G68.2
CH-8092 Zurich,
Switzerland
Courses:
Recent Research Papers:
- From qd to LR and QR, or, How were the qd and LR algorithms discovered?
(with Beresford N. Parlett)[Aug. 2009/July 2009]
(submitted ms.,
extended version)
- IDR explained
[Dec. 2008/Oct. 2009; to appear in Electr. Trans. Numer. Anal.]
(b/w,
color)
- How to make Simpler GMRES and GCR more stable
(with Pavel Jiranek and Miroslav Rozloznik) [Oct. 2007/Aug. 2008;
SIAM J. Matrix Anal. Appl. 30, 1483--1499 (2008)]
(Final version:
SIMAX)
- Numerical Analysis in Zurich --- 50 years ago
[Mar. 2007; Zurich Intelligencer, Springer-Verlag, July 2007]
(Proof)
- The block grade of a block Krylov space (with Th. Schmelzer)
[July 2006/July 2008; Linear Algebra Appl. 430, 174--185 (2009)]
(Final version:
LAA )
- A Brief Introduction to Krylov Space Methods for Solving
Linear Systems
[Feb. 2006; Frontiers of Computational Science --- Proceedings of the
International Symposium on Frontiers of Computational Science 2005
(Y. Kaneda, H. Kawamura, and M. Sasai, eds.), pages 53-62,
Springer-Verlag, Berlin Heidelberg, Mar. 2007]
(Preprint)
- Updating the QR decomposition of block tridiagonal and block
Hessenberg matrices (with Th. Schmelzer)
[Nov. 2005, rev. Mar. 2007, online Apr. 2007; Appl. Num. Math. 58,
871--883 (2008)]
(Final version:
APNUM)
- Block Krylov Space Methods for Linear Systems With
Multiple Right-hand Sides: an Introduction
[Aug. 2005; in: Modern Mathematical Models, Methods and Algorithms for
Real World Systems (A.H. Siddiqi, I.S. Duff, and O. Christensen, eds.),
pages 420-447, Anamaya Publishers, New Delhi, India, 2007]
(Preprint)
- A General Framework for Recursions for Krylov Space Solvers
[Aug. 2005]
(Preprint)
- A QR-decomposition of block tridiagonal matrices generated by the
block Lanczos process (with Th. Schmelzer)
[May 2005; Proceedings IMACS World Congress 2005 (on CD only)]
(Final version)
- A framework for generalized conjugate gradient methods ---
with special emphasis on contributions by Rüdiger Weiss
(with M. Rozloznik)
[Dec. 2000; rev. Mar. 2001; Appl. Numer. Math. 41, 7--22 (2002)]
(Final version:
APNUM)
- Variations of Zhang's Lanczos-type product method
(with S. Röllin)
[Dec. 2000; rev. Mar. 2001; Appl. Numer. Math. 41, 119--133 (2002)]
(Preprint [PostScript compressed])
- The Chebyshev iteration revisited
[Dec. 2000; rev. Apr. 2001; Parallel Comput. 28, 263--283 (2002)]
(Preprint [PostScript compressed],
final version:
Parallel Comput.)
- By how much can residual minimization accelerate the convergence
of orthogonal residual methods? (with M. Rozloznik)
[Jul. 2000; rev. May 2001; Numer. Algor. 27, 189-213 (2001)]]
(Preprint [PostScript compressed])
- A matrix interpretation of the extended Euclidean algorithm
[Mar. 2000; rev. May 2000; in: Structured Matrices in
Mathematics, Computer Science, and Engineering, Vol. 1
(V. Olshevsky, ed.), pages 53-70, Contemporary Mathematics, Vol. 280,
American Mathematical Society, 2001]
(Preprint [PostScript compressed])
- On Lanczos-type methods for Wilson fermions [Nov. 1999; revised,
April 2000; in: Numerical Challenges in Lattice Quantum
Chromodynamics (A. Frommer et al., eds.), LNCSE, Vol. 15, Springer, 2000]
(Preprint [PostScript compressed])
- Residual smoothing techniques: do they improve the limiting accuracy of
iterative solvers? (with M. Rozloznik)
[Oct. 1999/May 2000; BIT 41, 86-114 (2001)]
(Preprint [PostScript compressed];
final:
BIT
)
- Theodorsen's integral equation
[Sep. 1999; Encyclopaedia of Mathematics, Supplement III (M. Hazewinkel, ed.),
pages 401-402,Kluwer, 2001]
(Preprint [PostScript compressed])
- Accuracy of two three-term and three two-term recurrences for Krylov
space solvers (with Z. Strakos)
[revised, Oct. 1999; SIAM J. Matrix Anal. 22, 213-229(2000)]
(Preprint [PostScript compressed];
final:
SIAM)
- Look-ahead procedures for Lanczos-type product methods based on three-term
Lanczos recurrences (with K.J. Ressel) [revised, Jul. 1999;
SIAM J. Matrix Anal. 21, 1051-1078 (2000)]
(Preprint [PostScript compressed];
final:
SIAM)
Older Preprints or Reprints Available:
- Copper Mountain Conference on Iterative Methods, 1990:
The unsymmetric Lanczos algorithms and their relations to Padé approximation,
continued fractions, and the qd algorithm
( Sections 1-6,
Section 7)
- Conference on the History of Scientific and Numeric Computation, 1987:
The pioneer days of scientific computing in Switzerland
(PostScript,
compressed)
Some Recent Talks:
- "IDR --- a brief introduction"
Talk presented in the Minisymposium "Induced Dimension Reduction (IDR) methods:
a family of efficient Krylov solvers" of the SIAM Conference on Applied Linear
Algebra (LA09), Monterey, CA, USA (Oct 27, 2009).
(PDF in beamer.sty)
- "Block and Band Lanczos Algorithms: a Review of Options"
Talk presented at the Autumn School "Future Developments in Model Order Reduction",
Terschelling, The Netherlands (Sep 22, 2009).
(PDF in beamer.sty)
- "IDR in Variations"
Talk presented at TU Berlin (Dec 16, 2008), WIAS Berlin (Jan 12, 2009),
TU Freiberg (Jan 16, 2009), TU Chemnitz (Jan 20, 2009), TU Hamburg-Harburg
(Jan 28, 2009).
(PDF in beamer.sty)
- "Modified Moments for Indefinite Weight Functions"
(a Tribute to a Fruitful Collaboration with Gene H. Golub)
My contribution to " Remembering Gene Golub Around the World",
presented in Leuven, February 29, 2008.
(
1. PDF handout in beamer.sty;
2. scanned slides from talk presented at Richard S. Varga's 60th birthday
meeting, Kent, OH, Mar. 31, 1989)
- "Krylov Space Solvers"
An introductory lecture stressing basic ideas; not a survey of methods.
Talk given at International Symposium on Frontiers of Computational Science,
Dec. 12-13, Nagoya, 2005.
(PDF in beamer.sty)
- "Block Krylov Space Solvers: a Survey"
A survey of selected work on block Krylov methods.
Talk given at Nagoya University, Dec. 8, 2005.
(PDF in beamer.sty)
- "Block Krylov Space Methods for Linear Systems With
Multiple Right-hand Sides"
Basic aspects of block Krylov methods; effects of deflation in block GMRES
and in symmetric block Lanczos.
Talk given at the Householder Symposium XVI, May 5-8, 2005,
Seven Springs Mountain, PA, and at the
Joint Workshop on Computational Chemistry and Numerical Analysis (CCNA2005),
Dec. 5-6, 2005, Tokyo.
(PDF in beamer.sty)
Some Older Talks:
- Phoenix, AZ, USA (Jan. 89), Umhlange Rocks, SA (Jul. 89), Copper Mtn., CO, USA (Apr. 90), ...:
"The unsymmetric Lanczos algorithms and their relations to Padé
approximation, continued fractions, and the qd algorithm"
(scans/PDF),
- Richard S. Varga's 60th birthday meeting, Kent, OH, Mar. 31, 1989:
"Modified Moments for Indefinite Weight Functions"
(scans/PDF)
- Householder Symposium 1990, Tylosand, Sweden:
"A Completed Theory of the Unsymmetric Lanczos Process and Related
Algorithms"
(scans/PDF)
- 50th Anniversary of the Institute/Seminar for Applied Mathematics, ETH Zurich (Nov. 18, 1998):
"Contributions to Numerical Analysis in the 1950ies"
(PostScript,
compressed)
- "The Conjugate Gradient Method"
(PostScript,
compressed,
two color figures:
CGFig.ps,
SteepDescFig.ps)
- "Lanczos-Type Solvers for Non-Hermitian Linear Systems"
(PostScript,
compressed)
Current Research Projects:
Personal Information: ( partly outdated)
Former functions:
Address information for former members of the SPS section of CSCS/SCSC
Present university positions of some former IPS/SCSC students and postdocs
Mathematical Genealogy:
(from
Gerard L.G. Sleijpen and
The Mathematics Genealogy Project)
- C. Felix (Christian) Klein, Bonn 1868
- C. L. Ferdinand (Carl Louis) Lindemann, Erlangen-Nürnberg 1873
- David Hilbert, Königsberg 1885
- Erhard Schmidt, Göttingen 1905, and
Ludwig Bieberbach, Göttingen 1910
- Heinz Hopf, Berlin 1925
- Eduard Stiefel, Zürich 1935
- Peter Henrici, Zürich 1953
- Martin H. Gutknecht, Zürich 1973
|
Latsis Symposium 2002 on Iterative Solvers for Large Linear Systems
("CG50--GG70")
In 1952, M. Hestenes and E. Stiefel published their seminal paper
``Methods of conjugate gradients for solving linear systems''
in J. Research Nat. Bur. Standards 49 (1952), 409--436''. This conference,
which was held at ETH Zurich February 18-21, 2002,
had the purpose to commemorate this event, review the early and later
developments, survey the tremendous impact of the CG paper, and discuss
current research in the area of Krylov space methods and their
preconditioning. Simultaneously, it hosted a celebration of Professor
Gene Golub's 70th birthday.
Transcribed remarks, lecture notes, and slides from the presentations
of Todd, Hochstrasser, and Bauer
Some pictures of the conference
50 years CG
celebration at NIST
Dianne O'Leary's article in the NIST centennial publication
A Century of Excellence in Measurements, Standards, and Technology,
A Chronicle of Selected NBS/NIST Publications, 1901-2000
Private Links:
Contact Information:
Office:
Home:
Zelgligasse 1
CH-4900 Langenthal
Switzerland |
Tel: +41 (62) 923-3019 |
